Question

Decide the intervals in which f(x) = sin⁴x+cos⁴x is increasing or intervals in which it is decreasing. x ∈(0,π/2).

Answer 1

Dear student:

Given: f:(0,π/2) —>R

f(x)= sin⁴x+cos⁴x

 For determining the intervals in which f is increasing and decreasing.

Find derivative of f(x)

then see the derivative in which f is positive and negative.

If it is positive then f is increasing

And if it is negative then f is decreasing.

See the attachment.